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Determine the sum of the first terms of the following geometric sequence
a. 7,14,28,..
b. 4,-8,16,..
c. 1000,100, 10,..


Sagot :

[tex]\sf\pink{.  . • ☆ . ° .• °:. *₊ ° . ☆.  . • ☆ . ° .• °:. *₊ ° . ☆}[/tex]

[tex]\pink{\mathbb{\huge{꧁ᬊᬁ~ANSWER~ᬊ᭄꧂}}}[/tex]

a. 7, 14, 28, ...

[tex]\sf\pink{ᯓ★}[/tex] First term (a) = [tex]\rm{\pink{7}}[/tex]

[tex]\sf\pink{ᯓ★}[/tex] Common ratio (r) = [tex]\rm{\pink{2}}[/tex]

[tex]\sf\pink{ᯓ★}[/tex] Sum of first 5 terms = 7 x [tex]\pink{\large{\frac{(1 ~-~ 2⁵)}{(1 ~- ~2)}}}[/tex] = [tex]\blue{\underline{\sf\pink{217}}}[/tex]

[tex]\sf\pink{╴╴╴╴╴⊹ꮺ˚ ╴╴╴╴╴⊹˚ ╴╴╴╴˚ೃ ╴╴}[/tex]

b. 4, -8, 16, ...

[tex]\sf\pink{ᯓ★}[/tex] First term (a) = [tex]\rm{\pink{4}}[/tex]

[tex]\sf\pink{ᯓ★}[/tex] Common ratio (r) = [tex]\rm{\pink{-2}}[/tex]

[tex]\sf\pink{ᯓ★}[/tex] Sum of first 4 terms = 4 x [tex]\pink{\large{\frac{(1 ~-~ (-2)⁴)}{(1 ~-~ (-2))}}}[/tex] = [tex]\blue{\underline{\sf\pink{-20}}}[/tex]

[tex]\sf\pink{╴╴╴╴╴⊹ꮺ˚ ╴╴╴╴╴⊹˚ ╴╴╴╴˚ೃ ╴╴}[/tex]

c. 1000, 100, 10, ...

[tex]\sf\pink{ᯓ★}[/tex] First term (a) = [tex]\rm{\pink{1000}}[/tex]

[tex]\sf\pink{ᯓ★}[/tex] Common ratio (r) = [tex]\rm{\pink{0.1}}[/tex]

[tex]\sf\pink{ᯓ★}[/tex] Sum of first 3 terms = 1000 x [tex]\pink{\large{\frac{(1~ -~ 0.1³)}{(1 ~- ~0.1)}}}[/tex] = [tex]\blue{\underline{\sf\pink{1109}}}[/tex]

[tex]\sf\pink{╴╴╴╴╴⊹ꮺ˚ ╴╴╴╴╴⊹˚ ╴╴╴╴˚ೃ ╴╴}[/tex]

Learn more about geometric sequence!

[tex]\sf\pink{ᯓ★}[/tex] https://brainly.ph/question/31357335

[tex]\bold{\small\pink{⋆˚࿔~ ashrieIIe~˚⋆}}[/tex] [tex]\pink{\heartsuit}[/tex]

[tex]\sf\pink{.  . • ☆ . ° .• °:. *₊ ° . ☆.  . • ☆ . ° .• °:. *₊ ° . ☆}[/tex]

Zjuidn

first terms what? first n terms?